Find the sum of first 22 terms of an A.P. in which d = 22 and a22 = 1

1.	Find the sum of first 22 terms of an A.P. in which d = 22 and a22 = 149.
Answer» Let the first term be taken as a. Given, a₂₂ = 149 and the common difference d = 22 Also, we know that a_n = a + ( n – 1) d So, the 22^nd term is given by a₂₂ = a + (22 – 1)d 149 = a + (21) (22) a = 149 – 462 a = – 313 Now, for the sum of term S_n = \(\frac{n}{2}\)[2a + (n − 1)d] Here, n = 22 S₂₂ = \(\frac{22}{2}\)[2(−313) + (22 − 1)(22)] = (11)[ – 626 + 462] = (11)[–164] = – 1804 Hence, the sum of first 22 terms for the given A.P. is S₂₂ = -1804

Find the sum of first 22 terms of an A.P. in which d = 22 and a22 = 149.

Answer»

Let the first term be taken as a.

Given,

a₂₂ = 149 and the common difference d = 22

Also, we know that

a_n = a + ( n – 1) d

So, the 22^nd term is given by

a₂₂ = a + (22 – 1)d

149 = a + (21) (22)

a = 149 – 462

a = – 313

Now, for the sum of term

S_n = \(\frac{n}{2}\)[2a + (n − 1)d]

Here, n = 22

S₂₂ = \(\frac{22}{2}\)[2(−313) + (22 − 1)(22)]

= (11)[ – 626 + 462]

= (11)[–164]

= – 1804

Hence, the sum of first 22 terms for the given A.P. is S₂₂ = -1804